Derivative Of Arctan
Formula
Below is shown arctan(tan(x)) in red and its derivative in blue. Note that the derivative is undefined for values of x for which cos(x) is equal to 0, which means at x = π/2 + k. π, where k is an integer. Derivative of arctan. What is the derivative of the arctangent function of x? The derivative of the arctangent function of x is equal to 1 divided by (1+x 2).
$dfrac{d}{dx}{, tan^{-1}{x}} ,=, dfrac{1}{1+x^2}$
Introduction
The inverse tangent function is written as $tan^{-1}{x}$ or $arctan{(x)}$ in inverse trigonometry, where $x$ represents a real number. The derivative of the tan inverse function is written in mathematical form in differential calculus as follows.
$(1) ,$ $dfrac{d}{dx}{, Big(tan^{-1}{(x)}Big)}$
$(2) ,$ $dfrac{d}{dx}{, Big(arctan{(x)}Big)}$
The differentiation of the inverse tan function with respect to $x$ is equal to the reciprocal of the sum of one and $x$ squared.
$implies$ $dfrac{d}{dx}{, Big(tan^{-1}{(x)}Big)}$ $,=,$ $dfrac{1}{1+x^2}$
Alternative forms
The differentiation of the tan inverse function can be written in terms of any variable. Here are some of the examples to learn how to express the formula for the derivative of inverse tangent function in calculus.
Derivative Of Arctan
$(1) ,$ $dfrac{d}{dy}{, Big(tan^{-1}{(y)}Big)}$ $,=,$ $dfrac{1}{1+y^2}$
$(2) ,$ $dfrac{d}{dl}{, Big(tan^{-1}{(l)}Big)}$ $,=,$ $dfrac{1}{1+l^2}$
$(3) ,$ $dfrac{d}{dz}{, Big(tan^{-1}{(z)}Big)}$ $,=,$ $dfrac{1}{1+z^2}$
Derivative Of Arctan(4x)
Derivative Of Arctanx/3
Proof
Derivative Of Arctan(x/a)
Learn how to derive the differentiation of the inverse tangent function from first principle.